Math question please answer ASAP

Question

An obstetrician uses the length of a foetus, measured by ultrasound, to determine the approximate age of the foetus to establish a due date for the mother. Suppose a 10-week old foetus measures 3.2 cm in length and a 20-week old foetus measures 15.2cm.

a. Find the equation that relates age (in weeks) to length (in centimetres), assuming that age is a linear function of foetal length.

b. Provide a detailed interpretation of the slope.

c. What would you estimate is the length of a foetus at 22 weeks?

Answer 1

A. In order to find the equation, it's important to imagine this as if it's on a graph. To graph something, you'll need an x and y. In this case, the x would the number of weeks, and the y would the length of the fetus (because it changes over the number of weeks). We are going to be looking for a slope, which can be calculated by using y/x. Thus, we calculate the change of y over the change of x.

y/x = (15.2cm-3.2cm) / (20weeks - 10weeks) = 1.2

Now that there's a slope, we have to plug in our slope into y=mx+b, the equation for a linear graph. Using one of the points given (10 weeks, 3.2cm), we will determine the y-intercept (b).

3.2cm = 1.2(10)+ b

3.2cm = 12 + b

3.2 - 12 = b

b = -8.8

Therefore, our answer for A is y = 1.2x - 8.8

B. The slope is the change in the length of the fetus over a period of weeks.

C. To find the fetus length at 22 weeks, simply plug in 22 as x from our equation in part A.

y = 1.2(22) - 8.8 = 17.6cm

The length at 22 weeks is going to be 17.6cm.

Please message me if you have any more questions! :-)